Alpha-shapes are often described intuitively using circular erasers or spoons with radius \(\alpha \)  [1]}, [2]}. In this analogy [1]}, [2]}, constructing an \(\alpha \) -shape is thought of as carving away from the convex hull of a point cloud whenever it is possible to do so without removing any data point. At the final stage, all of the eraser marks with curvature \(1/\alpha \)  are approximated as straight edges. In particular, given some set of points, an associated \(\alpha \) -shape is made up of points and edges representing the boundary of the point cloud [2]}. Depending on the value of the hyper-parameter \(\alpha \) , we can select how tightly the \(\alpha \) -shape fits our data. For finite \(\alpha > 0\) , the associated \(\alpha \) -shape is built by drawing an edge between two data points whenever we can place a ball of radius \(\alpha \)  in such a way that (1) the open ball contains no points in our data set, and (2) the two data points in question lie on the boundary of the closed ball [1]}.
